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Abstract:
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Analysis of basketball short charts has gained interest among coaches and statisticians to study shot patterns for their opponents and improve their team's defending ability during a game. The data represents a marked spatial-temporal point process with mark represents the outcome (made/missed) of the shot. Here, we develop a Bayesian log Gaussian Cox process model providing joint analysis of the spatial pattern locations and outcomes of shots across multiple games. For each game, we convert the shot charts into polar coordinates: distance to the basket and angle from the sideline, which are in turn modeled as realizations of spatial point processes. We build up a hierarchical model for the log intensity function using Gaussian processes, which incorporate spatially varying effects based on game-specific covariates . For posterior computation, we adopt a kernel convolution approach and develop an efficient Markov chain Monte Carlo (MCMC) algorithm. We illustrate the proposed method using simulation studies and a case study of Michael JordanÕ's shots data.
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